Analytic system and method for testing gears

Abstract

A gear roll-testing method directed to the analysis and display of gear-set performance data, including motion transmission error, as acquired on gear-set rolling testers or gear-box test fixtures and includes the analysis and visualization of this data in the time-domain, frequency domain, and hybrids thereof. The invention further includes fundamental improvements in core signal processing, analytical and signal processing sequences that allow the data to be explored in more insightful ways, methods of visualizing and reporting the data and results, and a man-machine user-interface paradigm to provide these functions and features with greater flexibility and utility.

What is claimed is: 
     
       1. A method of testing gears, said method comprising:
 providing a pair of gears comprising a first gear and a second gear, said first gear and said second gear being operable to roll in mesh with one another, 
 rolling said first gear with said second gear on a gear testing machine, said gear testing machine being configured with one or more sensors operable to provide an output signal indicative of a rolling characteristic of one or more gears, 
 producing at least one independent signal, said independent signal being at least one of a signal based on output from said one or more sensors or an analytically derived signal, 
 selecting at least one frame portion having a non-zero duration from said at least one independent signal, wherein each of said selected at least one frame portion is processed according to the following steps: 
 determining a set of model basis functions based on the selected frame portion, 
 projecting the selected frame portion onto said model basis functions to produce model coefficients, 
 determining a reconstructed model from said model coefficients and said model basis functions, 
 subtracting said reconstructed model from the selected frame portion to yield a residual, 
 wherein said method further comprises at least one of: 
 (a) displaying and analyzing said residual to identify quality characteristics of at least one of said first gear and said second gear, 
 accepting or rejecting said at least one of said first gear and said second gear based on said quality characteristics, 
 and 
 (b) displaying and analyzing said model coefficients or reconstructed model to identify quality characteristics of at least one of said first gear and said second gear, 
 accepting or rejecting said at least one of said first gear and said second gear based on said quality characteristics. 
 
     
     
       2. The method of  claim 1  wherein said model basis functions are determined from at least one of:
 (a) duration of the selected frame portion, 
 (b) gear ratio of said first gear and said second gear, 
 (c) fundamental harmonic frequencies produced by rotation of said first gear with said second gear or duration of a mesh period of said first gear in mesh with said second gear, 
 (d) a predetermined set of harmonics for each fundamental frequency, said set including zero, and 
 (e) a set of aperiodic basis functions defined over the duration of said selected frame portion, said set including zero. 
 
     
     
       3. The method of  claim 1  where said reconstructed model and said residual are continually reevaluated as additional information is obtained from the sensors during machine operation. 
     
     
       4. The method of  claim 1  where a plurality of said independent signals are sampled simultaneously at coincident intervals to facilitate direct correlation and comparison. 
     
     
       5. The method of  claim 1  where said at least one independent signal is collected at uniform temporal samples and are subsequently interpolated to produce a sequence of samples regularly spaced in the position of one of said first gear and said second gear. 
     
     
       6. The method of  claim 1  wherein displaying of a residual, reconstructed model, or a combination thereof comprises:
 (a) subdividing the selected frame portion into a plurality of contiguous signal segments of equal duration, with the duration equal to one or more of the following:
 1. one or more entire mesh periods, 
 2. one or more entire revolutions of any gear in the set, 
 
 (b) representing the signal segments as functions of one or more of the following:
 1. time, 
 2. position of one of the gears in the set, 
 3. frequency, by means of a Fourier transform, 
 
 (c) presenting the signal segment functions, aligned and overlaid on the same independent axis, as one or more of the following:
 1. traces of the signal segment functions, 
 2. traces of statistical variations of the signal segment functions, consisting of the arithmetic mean and/or variance, determined pointwise. 
 
 
     
     
       7. The method of  claim 1  wherein displaying of a residual, reconstructed model, or combination thereof of the two comprises:
 (a) subdividing the selected frame portion into a plurality of contiguous signal segments of equal duration, with the duration equal to one or more entire mesh periods, 
 (b) determining, for each signal segment, a scalar metric for each signal segment, consisting of one or more of:
 1. peak-to-peak variation, 
 2. root-mean-squared amplitude, 
 3. a temporal or rotational shift of the signal segment necessary to best align the signal segment with a reference, determined as either: the average of at least two segments or a subset of the reconstructed model with the same duration as the signal segments, 
 4. measures of similarity to a reference determined as either: the average of at least two segments or a subset of the reconstructed model with the same duration as the signal segments, consisting of one or more of the following: Pearson correlation coefficient and/or root mean squared error, 
 
 (c) assigning to each segment two indices, the first index corresponding to either:
 1. the number of entire revolutions of one of the first gear or the second gear observed in the segment signal prior to the start of the segment duration, or 
 2. the number of mesh periods observed prior to the start of the segment duration, modulo the number of teeth on said one of the first gear or the second gear, the second index corresponding to either: 
 3. the number of entire revolutions of the other of the first gear or the second gear observed in the segment signal prior to the start of the segment duration, or 
 4. the number of mesh periods observed prior to the start of the segment duration, modulo the number of teeth on the other of the first gear or the second gear, 
 
 (d) presenting the scalar metrics, mapped to a range of grayscale or color values, onto a two-dimensional image where one coordinate of the image corresponds to the first index and the other coordinate of the image corresponds to the second index. 
 
     
     
       8. The method of  claim 1  wherein displaying of a residual, reconstructed model, or combination thereof comprises:
 (a) subdividing the selected frame portion into a plurality of contiguous or overlapping signal segments of predetermined, equal duration, each indexed sequentially, 
 (b) representing, by means of a Fourier transform, the signal segments as spectral functions, 
 (c) determining, from the spectral functions, one or more of the following measures:
 1. magnitude, 
 2. log-magnitude, 
 3. phase, 
 4. phase drift, as the difference between actual phase and that predicted by advancing the phase of a preceding spectral function by the temporal or rotational separation between the two segments, 
 
 (d) presenting the spectral measures, with values mapped to a range of grayscale or color values, as a two-dimensional image where one coordinate of the image corresponds to the index of the segment and the other coordinate of the image corresponds to the frequency variable of the spectral function. 
 
     
     
       9. The method of  claim 1  wherein displaying comprises:
 traces of one or more of the residual, reconstructed model, or a combination thereof on a plot where the independent axis represents time or position of one of the first gear or the second gear in the gear set and the dependent axis represents amplitude of the displayed quantity. 
 
     
     
       10. The method of  claim 1  wherein displaying of model coefficients comprises:
 plotting one or more of:
 (a) a bar chart with one bar per coefficient, with a height proportional to the magnitude of the coefficient; 
 (b) one or more radial plots on which line segments are drawn, one per coefficient, emanating from the coordinate origin and having a length proportional to the complex magnitude of corresponding coefficients and an angle with the horizontal axis proportional to the complex phase of the corresponding coefficients. 
 
 
     
     
       11. The method of  claim 1  where displays and analytical results are retained on an electronic storage medium for recall, with display and comparison of more than one prior record accomplished by one or more of the following:
 (a) simultaneous adjacent presentation, 
 (b) sequential presentation with progression directed by user interaction, 
 (c) sequential presentation with automatic, animated progression. 
 
     
     
       12. A method of testing gears, said method comprising:
 providing a pair of gears comprising a first gear and a second gear, said first gear and said second gear being operable to roll in mesh with one another,
 rolling said first gear with said second gear on a gear testing machine, said gear testing machine being configured with one or more sensors operable to provide an output signal indicative of a rolling characteristic of one or more gears, 
 producing at least one independent signal, said independent signal being at least one of a signal based on output from said one or more sensors or an analytically derived signal, 
 selecting at least one frame portion having a non-zero duration from said at least one independent signal, wherein each of said selected at least one frame portion is processed according to the following steps: 
 determining a set of model basis functions based on the selected frame portion, 
 projecting the selected frame portion onto said model basis functions to produce model coefficients, 
 determining a reconstructed model from said model coefficients and said model basis functions, 
 subtracting said reconstructed model from the selected frame portion to yield a residual, 
 wherein said method further comprises at least one of: 
 displaying and analyzing said residual to identify quality characteristics of at least one of said first gear and said second gear, 
 accepting or rejecting said at least one of said first gear and said second gear based on said quality characteristics, 
 and 
 displaying and analyzing said model coefficients or reconstructed model to identify quality characteristics of at least one of said first gear and said second gear, 
 accepting or rejecting said at least one of said first gear and said second gear based on said quality characteristics, 
 said method being conducted in an always-on mode wherein the preceding steps are repeated and performed continuously as long as a coordinated motion between said pair of gears is detected by said one or more sensors and new frames of data can be filled. 
 
 
     
     
       13. The method of  claim 12  wherein the tooth ratio of said first and second gears being rolled is not known in advance in the always-on mode but the always-on mode determines the tooth ratio based on the real-time data it receives. 
     
     
       14. The method of  claim 12  wherein a user can observe information comprising at least one of measurements, displays, visualizations and results at any time when the always-on mode is operating, said information being available independent of whether any other testing mode is concurrently active. 
     
     
       15. The method of  claim 14  wherein said information comprising at least one of measurements, displays, visualizations and results includes at least one of:
 (a) amplitude and phasing of one or more harmonics of the frequency associated with a mesh period; 
 (b) average signal shape over the duration of one mesh period; 
 (c) gear runout harmonic amplitudes; 
 (d) average signal shape of gear runout; 
 (e) presence and location of tooth damage; 
 (f) average signal shape with pinion bases removed; and 
 (g) average signal shape with gear bases removed. 
 
     
     
       16. The method of  claim 12  further comprising interactively manipulating the displays to better examine aspects of the displayed data. 
     
     
       17. The method of  claim 12  wherein displays can be put on hold so that a current set of displayed data can be examined without being replaced by subsequent frames. 
     
     
       18. The method of  claim 12  wherein a current set of data can be captured and stored for retrieval or examination later and/or for comparison with current data. 
     
     
       19. The method of  claim 12  wherein differences between current data and stored reference or master data can be examined and visualized. 
     
     
       20. The method of  claim 12  wherein the always-on mode further comprises recognizing and localizing tooth damage on at least one of said first gear and said second gear without a requirement for separate set up of any testing parameters or settings, said always-on mode identifying part rotation or tooth indices that best represent the location of the recognized damage, said always-on mode automatically informing the user of such damage through textual messaging and/or graphical displays.